It sounds as if there is a file that has not been removed during the uninstall process that is somehow blocking the process.
Have you tried running Ccleaner and/or RegScrubXp to resolve the situation? You should unplug all peripherals - especially the modem - befor doing this.
It may be worthwhile running the cleaners in Safe Mode in case the file you need to remove is `live` (running) and can`t be removed as a result.
If this fails it may be worthwhile looking at Task Manager and attempting to identify any files associated with the modem and closing them before running the cleaners again.
You could also search your `Programs` folder for any folder associated with the modem and delete that as well. If it refuses to be deleted, try moving the folder to another location, renaming it, rebooting the PC and seeing if it can then be deleted. If this works then running the cleaners again should remove any remaining reference. Hopefully the modem should then be able to complete a clean installation.
Whether this will resolve your other problems I don`t know but you can let us know.